Question

Marie is logging the number of radioactive isotopes she observes every minute. She has determined her function to be f(x) = -4x + 120. Based on the situation, describe any necessary restrictions to the domain and range and provide justification or the restrictions

Answer 1

If f(x) represents the # of radioactive isotopes present, then f(x) must always be 120 or less, down to zero.  f(x) is zero when x = 30.  Thus, the range  is [0,120], and the domain is [0,30].  The domain represents time measurements; we assume we begin at x=0, and then determine at what value of x the function f(x) will reach zero.